Question

Factorise the following:

x(6x – 7) – 5

Answer 1

Given expression: x(6x – 7) – 5

Step-wise calculation:

1. Expand the expression inside the parentheses:

x × 6x = 6x² and x × (–7) = –7x

So, the expression becomes 6x² – 7x – 5.

2. Now, factorize the quadratic trinomial 6x² – 7x – 5.

We look for two numbers whose product is 6 × (–5) = –30 and whose sum is –7.

These numbers are –10 and 3 because –10 × 3 = –30 and –10 + 3 = –7.

3. Rewrite the middle term –7x using these two numbers:

6x² – 10x + 3x – 5

4. Group the terms:

(6x² – 10x) + (3x – 5)

5. Factor out the common factor from each group:

2x(3x – 5) + 1(3x – 5)

6. Factor out the common binomial factor (3x – 5):

(3x – 5)(2x + 1)